Q1 (25 pts) A heated process is used to heat a semiconductor wafer operating with first-order dynamics, that is, the transfer function relating changes in temperature T to changes in the heater input power level P is T'(s) K P's TS +1 where K has units [C/Kw] and 7 has units [minutes). The process is at steady state when an engineer changes the power input stepwise from 1 to 1.5 Kw. She notes the following: (i) The process temperature initially is 80C. (ii) Four minutes after changing the power input, the temperature is 230C. (iii) Thirty minutes later the temperature is 280C. (a) What are K and 7 in the process transfer function? (b) If at another time the engineer changes the power input linearly at a rate of 0.5kW/min, what can you say about the maximum rate of change of process temperature: When will it occur? How large will it be